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1 + 3 + 5 + 7 = 16 = 4².
Sum of first n odd numbers = n². Thus, 6² = 36.
Sum of first 8 odd numbers = 8² = 64.
36² = 35² + 71 = 1225 + 71 = 1296.
nth odd number = 2n − 1 = 2×40 − 1 = 79.
64 = 8².
11² − 10² − 1 = 121 − 100 − 1 = 20.
21² − 20² − 1 = 441 − 400 − 1 = 40.
3 + 6 = 9 = 3².
7 × 7 = 49.
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